Simplifying Radicals: Variables, Exponents, and Fractions

What is the simplified form of the square root of x to the fifth power?

• sqrt(x^5)

• x^3

• x^2 * sqrt(x)

• x^2

How many times does 2 go into 7 when simplifying the square root of x to the seventh power?

• 2 times with 1 remaining

• 3 times with 1 remaining

• 3 times with no remainder

• 4 times with 1 remaining

What is the simplified form of the square root of 32?

• 4 * sqrt(2)

• 5 * sqrt(2)

• 4 * sqrt(8)

• 2 * sqrt(16)

When simplifying the square root of 50x^3y^18, what is the simplified form of the square root of 50?

• 2 * sqrt(25)

• 25 * sqrt(2)

• 10 * sqrt(5)

• 5 * sqrt(2)

How many times does 3 go into 14 when simplifying the cube root of x^14?

• 3 times with 2 remaining

• 4 times with 2 remaining

• 5 times with 1 remaining

• 4 times with 1 remaining

What is the simplified form of the cube root of 16?

• 2 * cube root(2)

• 4 * cube root(2)

• 2 * cube root(8)

• 8 * cube root(2)

When simplifying the square root of 75x^7y^3z^10 over 8x^3y^9z^4, what is the simplified form of the square root of 75?

• 5 * sqrt(3)

• 10 * sqrt(3)

• 25 * sqrt(3)

• 3 * sqrt(25)

What is the simplified form of the square root of 75x^7y^3z^10 over 8x^3y^9z^4?

• 5x^2|z^3|sqrt(6) / 4|y^3|

• 5x^2|z^3|sqrt(3) / 4|y^3|

• 5x^2|z^3|sqrt(6) / 2|y^3|

• 5x^2|z^3|sqrt(3) / 2|y^3|

What is the simplified form of the cube root of 16x^7y^4z^9 over 54x^2y^9z^15?

• 2x * cube root(x^2y) / 3y^3z^3

• 2x * cube root(x^2y) / 3y^2z^3

• 2x * cube root(x^2y) / 3y^3z^2

• 2x * cube root(x^2y) / 3y^2z^2

What is the simplified form of the cube root of 8?

• 2

• 3

• 4

• 8